TY - JOUR
TI - Numerical solution for stochastic heat equation with Neumann boundary conditions
AU - Raja Balachandar S
AU - Uma D
AU - Jafari H
AU - Venkatesh S G
JN - Thermal Science
PY - 2023
VL - 27
IS - 101
SP - 57
EP - 66
PT - Article
AB - In this article, we propose a new technique based on 2-D shifted Legendre  poly­nomials through the operational matrix integration method to find the  numeri­cal solution of the stochastic heat equation with Neumann boundary  conditions. For the proposed technique, the convergence criteria and the  error estima­tion are also discussed in detail. This new technique is tested  with two exam­ples, and it is observed that this method is very easy to  handle such problems as the initial and boundary conditions are taken care  of automatically. Also, the time complexity of the proposed approach is  discussed and it is proved to be O[k(N + 1)4] where N denotes the degree of  the approximate function and k is the number of simulations. This method is  very convenient and efficient for solving other partial differential  equations.